Prime Minister Najib Razak of Malaysia in Kuala Lumpur on Thursday. A spokesman said he had not changed his position that the hundreds of millions in his personal accounts came from an unidentified Saudi donor, not a government investment fund that he oversaw.Credit...Mohd Rasfan/Agence France-Presse — Getty Images

BANGKOK — A United States Justice Department complaint filed in federal court this week directly contradicts repeated assertions by the Malaysian prime minister, Najib Razak, about the origins and purpose of hundreds of millions of dollars that ended up in his personal bank accounts.

While Mr. Najib and other Malaysian officials have insisted that the money was a gift from an unidentified Saudi donor, the Justice Department said that it was stolen from a Malaysian government investment fund that Mr. Najib oversaw. Mr. Najib has said he never received any money from the fund.

The court filing, one of several complaints filed Wednesday in a federal money-laundering investigation, provides the first official public documentation of transactions that challenge Mr. Najib’s version of events in a scandal that has battered his government for the past year.

The revelations could undermine his credibility and give new ammunition to a movement to force him from office. However, he maintains firm control over his governing party and has successfully stifled opposition with the firing of critics from party posts, the closing of online news outlets and the criminal prosecution of social media detractors and political opponents.

Mr. Najib, who has acknowledged receiving the money but said he broke no laws and took nothing for personal gain, told reporters on Thursday that his government would “fully cooperate” with the Justice Department action.

“Allow the process to take its course,” he said, “but I want to say categorically that we are serious about good governance.”

A spokesman for Mr. Najib, reached late Thursday, said that the prime minister had not changed his position that the money he received was a gift from a Saudi donor and that he gave most of it back because he did not need it.

The Justice Department complaint alleges in 136 pages of blow-by-blow detail that huge sums were diverted from the government fund, routed through bank accounts in various countries and then spent on high-end real estate, artwork, gambling and various luxury goods by Mr. Najib’s stepson, friends and associates.

The court filing seeks to recover more than $1 billion in assets bought with money that prosecutors say was stolen from the fund, known as 1Malaysia Development Berhad, or 1MDB.

Those assets, Attorney General Loretta E. Lynch said Wednesday, “are just a portion of the more than $3 billion that was stolen from 1MDB and laundered through American financial institutions in violation of United States law.”

The case, she said, should be seen as a sign of the country’s “firm commitment to fighting international corruption” and the department’s determination “to protect the American financial system from being used as a conduit for corruption.”

The United States is among several governments, including Malaysia, Singapore and Switzerland, that have investigated 1MDB. The inquiries began last year after an investigative report in The New York Times traced the purchases of about $150 million in residential properties and artwork in the United States to relatives or associates of Mr. Najib.

While the federal complaint does not identify Mr. Najib by name, it cites $731 million in funds that came from 1MDB that were deposited into accounts belonging to a government official identified as “Malaysian Official 1.”

However, Mr. Najib is clearly recognizable in the descriptions and actions attributed to that official.

Large transactions by “Malaysian Official 1” described in the complaint are identical to those previously acknowledged by Mr. Najib. The complaint describes the official’s role in managing the fund, which matches Mr. Najib’s role. And it says “Malaysian Official 1” is a relative of Riza Aziz, Mr. Najib’s stepson.

A person with knowledge of the case, who spoke on the condition of anonymity because he was not authorized to speak publicly, confirmed that “Malaysian Official 1” was Mr. Najib.

The complaint does name Mr. Aziz, and a family friend, Jho Low, who played a key role in establishing the fund. Both are cited as possessing assets bought with money stolen from 1MDB.

Mr. Najib’s advisers have said Mr. Najib received about $1 billion in 2013, most of it donations from a member of the Saudi royal family to help him fight a tough election campaign that year.

That explanation of a Saudi gift was repeated by Mr. Najib’s attorney general, Mohamed Apandi Ali, who closed a government investigation into the money in January saying that he had found no evidence of wrongdoing.

On Thursday, Mr. Apandi issued a statement asserting that no investigation had found evidence that 1MDB funds had been misappropriated. He said he had “strong concerns at the insinuations and allegations” against Mr. Najib in the Justice Department complaint.

The Saudi gift was also confirmed by Saudi Arabia.

Foreign Minister Adel al-Jubeir told reporters in April that Mr. Najib had received a “genuine donation” from a Saudi donor. He did not specify the amount or provide any details.

A Saudi Foreign Ministry spokesman did not respond Friday to requests for comment.

The Justice Department complaint mentions no such gift.

The complaint says that $681 million transferred to Mr. Najib in 2013 came from a Singapore bank account held in the name of Tanore Finance Corporation. It says the money originated from $3 billion in bonds underwritten for 1MDB by Goldman Sachs.

The Singapore account was controlled by Tan Kim Loong, also known as Eric Tan, an associate of Mr. Low, the complaint says.

Four months after receiving the $681 million, Mr. Najib transferred $620 million back to the same Tanore account, according to the complaint.

The complaint offers no explanation for why the prime minister received the money, held it for four months, then returned part of it. It is also unclear what happened to the $61 million he kept, although advisers have said he needed money for parliamentary elections that year.

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Loretta E. Lynch, the United States attorney general, announcing the filing of complaints seeking more than $1 billion in assets bought with money prosecutors say was stolen from a Malaysian government investment fund.Credit...James Lawler Duggan/Reuters

Mr. Low and Mr. Tan used money from the Tanore account to buy expensive artwork and an interest in the Park Lane Hotel, a luxury hotel overlooking Central Park in Manhattan, the complaint says.

The complaint also says that “Malaysian Official 1” received $20 million in stolen 1MDB funds in 2011. The money, the first he received from the fund, was transferred from an account held in the name of a Saudi prince, the complaint says. It does not identify the prince.

He received $30 million in 1MDB money in 2012 from a separate account, the complaint says.

The prime minister’s office did not respond to inquiries about those two deposits.

The two transactions bring to $731 million the amount of money Mr. Najib is said to have received from the government fund he oversaw.

Mr. Najib created 1MDB in 2009 to promote Malaysia’s economic development. He oversaw the fund as chairman of its advisory board, a position he recently relinquished, and as finance minister, a position he still holds. The fund is wholly owned by the Finance Ministry.

The fund’s goal was “improving the well-being of the Malaysian people,” Ms. Lynch said in announcing the civil action. “But unfortunately, sadly, tragically, a number of corrupt 1MDB officials treated this public trust as a personal bank account.”

The F.B.I. and the Internal Revenue Service took part in the investigation and relied in part on bank transfer data, 1MDB memos and internal emails. Special Agent Darryl Wegner, chief of the F.B.I.’s International Corruption Unit, said that leaders of the Malaysian Anti-Corruption Commission showed “tremendous courage” in pursuing the investigation.

The Malaysian Anti-Corruption Commission’s investigation was shut down by Malaysia’s attorney general.

In Washington, the White House spokesman Josh Earnest said Thursday that President Obama had discussed the scandal with Mr. Najib during a visit to Malaysia last fall.

“The president reiterated how important it is, particularly for a fast-growing country like Malaysia, to be transparent, to demonstrate a commitment to fair play and good government and a business climate that will allow that country’s economy to continue to succeed,” Mr. Earnest said.